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Suncica Canic - One of the best experts on this subject based on the ideXlab platform.

  • analysis of a 3d nonlinear moving Boundary problem describing Fluid mesh shell interaction
    arXiv: Analysis of PDEs, 2019
    Co-Authors: Suncica Canic, Marija Galic, Boris Muha
    Abstract:

    We consider a nonlinear, moving Boundary, Fluid-structure interaction problem between a time dependent incompressible, viscous Fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The Fluid flow is modeled by the time-dependent Navier-Stokes equations in a three-dimensional cylindrical domain, while the lateral wall of the cylinder is modeled by the two-dimensional linearly elastic Koiter shell equations coupled to a one-dimensional system of conservation laws defined on a graph domain, describing a mesh of curved rods. The mesh supported shell allows displacements in all three spatial directions. Two-way coupling based on kinematic and dynamic coupling conditions is assumed between the Fluid and composite structure, and between the mesh of curved rods and Koiter shell. Problems of this type arise in many applications, including blood flow through arteries treated with vascular prostheses called stents. We prove the existence of a weak solution to this nonlinear, moving-Boundary problem by using the time discretization via Lie operator splitting method combined with an Arbitrary Lagrangian-Eulerian approach, and a non-trivial extension of the Aubin-Lions-Simon compactness result to problems on moving domains.

  • existence of a weak solution to a Fluid elastic structure interaction problem with the navier slip Boundary condition
    Journal of Differential Equations, 2016
    Co-Authors: Boris Muha, Suncica Canic
    Abstract:

    Abstract We study a nonlinear, moving Boundary Fluid–structure interaction (FSI) problem between an incompressible, viscous Newtonian Fluid, modeled by the 2D Navier–Stokes equations, and an elastic structure modeled by the shell or plate equations. The Fluid and structure are coupled via the Navier slip Boundary condition and balance of contact forces at the Fluid–structure interface. The slip Boundary condition might be more realistic than the classical no-slip Boundary condition in situations, e.g., when the structure is “rough”, and in modeling FSI dynamics near, or at a contact. Cardiovascular tissue and cell-seeded tissue constructs, which consist of grooves in tissue scaffolds that are lined with cells, are examples of “rough” elastic interfaces interacting with an incompressible, viscous Fluid. The problem of heart valve closure is an example of a FSI problem with a contact involving elastic interfaces. We prove the existence of a weak solution to this class of problems by designing a constructive proof based on the time discretization via operator splitting. This is the first existence result for Fluid–structure interaction problems involving elastic structures satisfying the Navier slip Boundary condition.

  • existence of a weak solution to a Fluid elastic structure interaction problem with the navier slip Boundary condition
    arXiv: Analysis of PDEs, 2015
    Co-Authors: Boris Muha, Suncica Canic
    Abstract:

    We study a nonlinear, moving Boundary Fluid-structure interaction problem between an incompressible, viscous Newtonian Fluid, modeled by the 2D Navier-Stokes equations, and an elastic structure modeled by the shell or plate equations. The Fluid and structure are coupled via the {\em Navier slip Boundary condition} and balance of contact forces at the Fluid-structure interface. The slip Boundary condition is more realistic than the classical no-slip Boundary condition in situations, e.g., when the structure is "rough", and in modeling dynamics near, or at a contact. Cardiovascular tissue and cell-seeded tissue constructs, which consist of grooves in tissue scaffolds that are lined with cells, are examples of "rough" elastic interfaces interacting with and incompressible, viscous Fluid. The problem of heart valve closure is an example of a Fluid-structure interaction problem with a contact. We prove the existence of a weak solution to this class of problems by designing a constructive proof based on the time discretization via operator splitting. This is the first existence result for Fluid-structure interaction problems involving elastic structures satisfying the Navier slip Boundary condition

  • existence of a solution to a Fluid multi layered structure interaction problem
    Journal of Differential Equations, 2014
    Co-Authors: Boris Muha, Suncica Canic
    Abstract:

    Abstract We study a nonlinear, unsteady, moving Boundary, Fluid–structure interaction (FSI) problem in which the structure is composed of two layers: a thick layer, and a thin layer which serves as a Fluid–structure interface with mass. The Fluid flow, which is driven by the time-dependent dynamic pressure data, is modeled by the Navier–Stokes equations for an incompressible, viscous Fluid, defined on a 2D cylinder. The elastodynamics of the cylinder wall is governed by the 1D linear wave equation modeling the thin structural layer, and by the 2D equations of linear elasticity modeling the thick structural layer. We prove existence of a weak solution to this nonlinear FSI problem as long as the cylinder radius is greater than zero. The spaces of weak solutions presented in this manuscript reveal a striking new feature: the presence of a thin Fluid–structure interface with mass regularizes solutions of the coupled problem.

  • existence of a solution to a Fluid multi layered structure interaction problem
    arXiv: Analysis of PDEs, 2013
    Co-Authors: Boris Muha, Suncica Canic
    Abstract:

    We study a nonlinear, unsteady, moving Boundary, Fluid-structure (FSI) problem in which the structure is composed of two layers: a thin layer which is in contact with the Fluid, and a thick layer which sits on top of the thin structural layer. The Fluid flow, which is driven by the time-dependent dynamic pressure data, is governed by the 2D Navier-Stokes equations for an incompressible, viscous Fluid, defined on a 2D cylinder. The elastodynamics of the cylinder wall is governed by the 1D linear wave equation modeling the thin structural layer, and by the 2D equations of linear elasticity modeling the thick structural layer. The Fluid and the structure, as well as the two structural layers, are fully coupled via the kinematic and dynamic coupling conditions describing continuity of velocity and balance of contact forces. The thin structural layer acts as a Fluid-structure interface with mass. The resulting FSI problem is a nonlinear moving Boundary problem of parabolic-hyperbolic type. This problem is motivated by the flow of blood in elastic arteries whose walls are composed of several layers, each with different mechanical characteristics and thickness. We prove existence of a weak solution to this nonlinear FSI problem as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme. We effectively prove convergence of that numerical scheme to a solution of the nonlinear Fluid-multi-layered-structure interaction problem. The spaces of weak solutions presented in this manuscript reveal a striking new feature: the presence of a thin Fluid-structure interface with mass regularizes solutions of the coupled problem.

Boris Muha - One of the best experts on this subject based on the ideXlab platform.

  • A Uniqueness Result for 3D Incompressible Fluid-Rigid Body Interaction Problem
    Journal of Mathematical Fluid Mechanics, 2020
    Co-Authors: Boris Muha, Šárka Nečasová, Ana Radošević
    Abstract:

    We study a 3D nonlinear moving Boundary Fluid-structure interaction problem describing the interaction of the Fluid flow with a rigid body. The Fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations called Euler equations for the rigid body. The equations are fully coupled via dynamical and kinematic coupling conditions. We consider two different kinds of kinematic coupling conditions: no-slip and slip. In both cases we prove a generalization of the well-known weak-strong uniqueness result for the Navier-Stokes equations to the Fluid-rigid body system. More precisely, we prove that weak solutions that additionally satisfy the Prodi-Serrin $$\text {L}^{r}-\text {L}^{s}$$ L r - L s condition are unique in the class of Leray-Hopf weak solutions.

  • existence of a weak solution to a Fluid elastic structure interaction problem with the navier slip Boundary condition
    Journal of Differential Equations, 2016
    Co-Authors: Boris Muha, Suncica Canic
    Abstract:

    Abstract We study a nonlinear, moving Boundary Fluid–structure interaction (FSI) problem between an incompressible, viscous Newtonian Fluid, modeled by the 2D Navier–Stokes equations, and an elastic structure modeled by the shell or plate equations. The Fluid and structure are coupled via the Navier slip Boundary condition and balance of contact forces at the Fluid–structure interface. The slip Boundary condition might be more realistic than the classical no-slip Boundary condition in situations, e.g., when the structure is “rough”, and in modeling FSI dynamics near, or at a contact. Cardiovascular tissue and cell-seeded tissue constructs, which consist of grooves in tissue scaffolds that are lined with cells, are examples of “rough” elastic interfaces interacting with an incompressible, viscous Fluid. The problem of heart valve closure is an example of a FSI problem with a contact involving elastic interfaces. We prove the existence of a weak solution to this class of problems by designing a constructive proof based on the time discretization via operator splitting. This is the first existence result for Fluid–structure interaction problems involving elastic structures satisfying the Navier slip Boundary condition.

  • existence of a weak solution to a Fluid elastic structure interaction problem with the navier slip Boundary condition
    arXiv: Analysis of PDEs, 2015
    Co-Authors: Boris Muha, Suncica Canic
    Abstract:

    We study a nonlinear, moving Boundary Fluid-structure interaction problem between an incompressible, viscous Newtonian Fluid, modeled by the 2D Navier-Stokes equations, and an elastic structure modeled by the shell or plate equations. The Fluid and structure are coupled via the {\em Navier slip Boundary condition} and balance of contact forces at the Fluid-structure interface. The slip Boundary condition is more realistic than the classical no-slip Boundary condition in situations, e.g., when the structure is "rough", and in modeling dynamics near, or at a contact. Cardiovascular tissue and cell-seeded tissue constructs, which consist of grooves in tissue scaffolds that are lined with cells, are examples of "rough" elastic interfaces interacting with and incompressible, viscous Fluid. The problem of heart valve closure is an example of a Fluid-structure interaction problem with a contact. We prove the existence of a weak solution to this class of problems by designing a constructive proof based on the time discretization via operator splitting. This is the first existence result for Fluid-structure interaction problems involving elastic structures satisfying the Navier slip Boundary condition

  • existence of a solution to a Fluid multi layered structure interaction problem
    Journal of Differential Equations, 2014
    Co-Authors: Boris Muha, Suncica Canic
    Abstract:

    Abstract We study a nonlinear, unsteady, moving Boundary, Fluid–structure interaction (FSI) problem in which the structure is composed of two layers: a thick layer, and a thin layer which serves as a Fluid–structure interface with mass. The Fluid flow, which is driven by the time-dependent dynamic pressure data, is modeled by the Navier–Stokes equations for an incompressible, viscous Fluid, defined on a 2D cylinder. The elastodynamics of the cylinder wall is governed by the 1D linear wave equation modeling the thin structural layer, and by the 2D equations of linear elasticity modeling the thick structural layer. We prove existence of a weak solution to this nonlinear FSI problem as long as the cylinder radius is greater than zero. The spaces of weak solutions presented in this manuscript reveal a striking new feature: the presence of a thin Fluid–structure interface with mass regularizes solutions of the coupled problem.

  • existence of a solution to a Fluid multi layered structure interaction problem
    arXiv: Analysis of PDEs, 2013
    Co-Authors: Boris Muha, Suncica Canic
    Abstract:

    We study a nonlinear, unsteady, moving Boundary, Fluid-structure (FSI) problem in which the structure is composed of two layers: a thin layer which is in contact with the Fluid, and a thick layer which sits on top of the thin structural layer. The Fluid flow, which is driven by the time-dependent dynamic pressure data, is governed by the 2D Navier-Stokes equations for an incompressible, viscous Fluid, defined on a 2D cylinder. The elastodynamics of the cylinder wall is governed by the 1D linear wave equation modeling the thin structural layer, and by the 2D equations of linear elasticity modeling the thick structural layer. The Fluid and the structure, as well as the two structural layers, are fully coupled via the kinematic and dynamic coupling conditions describing continuity of velocity and balance of contact forces. The thin structural layer acts as a Fluid-structure interface with mass. The resulting FSI problem is a nonlinear moving Boundary problem of parabolic-hyperbolic type. This problem is motivated by the flow of blood in elastic arteries whose walls are composed of several layers, each with different mechanical characteristics and thickness. We prove existence of a weak solution to this nonlinear FSI problem as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme. We effectively prove convergence of that numerical scheme to a solution of the nonlinear Fluid-multi-layered-structure interaction problem. The spaces of weak solutions presented in this manuscript reveal a striking new feature: the presence of a thin Fluid-structure interface with mass regularizes solutions of the coupled problem.

Liliane Léger - One of the best experts on this subject based on the ideXlab platform.

  • slip transition of a polymer melt under shear stress
    Physical Review Letters, 1993
    Co-Authors: Kalman B Migler, H Hervet, Liliane Léger
    Abstract:

    We present the first direct measurements of the local velocity of a sheared polymer melt within the first 100 nm from the solid-liquid interface. For high enough shear rates we observe a sharp transition between weak and strong slip (i.e., a nonzero Boundary Fluid velocity) in the case of weak polymer-surface interactions [polydimethylsiloxane (PDMS) on silanated silica surfaces]. For strong polymersurface interactions the slip is strongly reduced. These results are compared to a theoretical model recently proposed by Brochard and de Gennes

Janos Urai - One of the best experts on this subject based on the ideXlab platform.

  • the interaction of migrating grain boundaries and Fluid inclusions in naturally deformed quartz a case study of a folded and partly recrystallized quartz vein from the hunsruck slate germany
    Journal of Structural Geology, 2011
    Co-Authors: Joyce Schmatz, Janos Urai
    Abstract:

    Abstract We studied the microstructure of a folded and partly recrystallized quartz vein from the Hunsruck Slates in Germany, focusing on the morphology and distribution of Fluid inclusions in the old and new grains and along the different types of grain boundaries. Blocky vein quartz grains show undulose extinction and develop subgrains. New grains form by subgrain rotation and grain Boundary migration, with a bimodal size distribution. The old, deformed grains contain numerous, complex, H2O–CO2–graphite inclusions, with significant differences in Fluid inclusion setting along subgrain boundaries. The new grains have a lower content of H2O-rich inclusions than the old grains and do not contain graphite, and there is a significant difference in volume and density of Fluid inclusions between the large and small new grains. Grain boundaries between old and new grains are irregular, containing similar Fluid inclusions as the old grains, but no enrichment in graphite, while grain boundaries between new grains are smooth and can be inclusion-free or contain arrays of Fluid inclusions. We interpret these structures to have formed by a series of complex interactions between grain boundaries migrating at different velocity and the Fluid inclusions. Differences in mobility and grain Boundary velocity can result in different variations of drag and drop- interaction, while chemical differences lead to phase separation during grain Boundary–Fluid interaction. Migration of grain boundaries into the old grains was accompanied by significant redistribution of Fluids and graphite along the grain Boundary together with oxidation of graphitic inclusions to CO2.

Joseph F Sadorski - One of the best experts on this subject based on the ideXlab platform.

  • Fluid controlled grain Boundary migration and switch in slip systems in a high strain high temperature contact aureole california usa
    Tectonophysics, 2016
    Co-Authors: Sven Morgan, Peter I Nabelek, James J Student, Joseph F Sadorski
    Abstract:

    Abstract Within the highly strained aureole surrounding the Eureka Valley–Joshua Flat–Beer Creek (EJB) composite pluton of eastern California, an inversion in microstructures and crystallographic preferred orientations (CPOs) exists with distance from the contact. An inner aureole ( slip in quartz. Within the outer aureole (250 m to 1500 m from the contact), quartzites are interbedded with pelitic schist and are completely recrystallized and microstructures are indicative of extensive GBM. CPOs are indicative of prism [c] slip. Oxygen isotope ratios in the inner aureole are only slightly shifted from their original values. Oxygen isotopes from the outer aureole are shifted more, which is consistent with equilibration with locally derived Fluids. We suggest that recrystallization in the outer aureole was aided by pore water, water derived from Fluid inclusions, and water generated by prograde reactions in the schists. The pore Fluids in the inner aureole were also probably initially water-rich. However, during prograde reactions in the intervening calc-silicate rocks, and perhaps more importantly, between calcite cement and quartz in the quartzites, the pore Fluid composition in the inner aureole changed to become dominated by CO 2 , which acted as a non-wetting phase and decreased the fugacity of water slowing grain Boundary mobility. Low water fugacity also suppressed the activity of prism [c] slip. Therefore, we propose that dry conditions or a grain Boundary Fluid with a significant non-wetting component (CO 2 ) can result in apparent temperatures of deformation that are more than 100 °C lower than the real temperatures of deformation.